There is a well-known game of logic in which the subject is presented with a beam-type balance scale and twelve coins, each of which seems to be of the same color, texture, size and weight as the others. In fact, one of the coins is somewhat heavier or lighter in weight than each of the other eleven. The object of the game is to determine, in no more than three weighings, both which coin is the odd one and whether it is heavier or lighter in weight.
In the paperback book More Games for the Super-Intelligent, by James F. Fixx, 1SBN 0-445-04144-5, a typical statement of this game of logic is set forth on pages 88 and 89, and on pages 139 and 140 a typical classical solution is given.
Also of interest is the U.S. patent of Wilcox, U.S. Pat. No. 4,014,550, issued Mar. 29, 1977. Although this patent primarily relates to an electronic version of the game, the classical version is set forth at column 1, lines 15-23 and column 2, lines 26-29 (the problem) and at column 4, lines 25-29 (the solution).
A particular balance for use in conducting the game is shown in the U.S. patent of Dunson, U.S. Pat. No. 3,424,455, issued Jan. 28, 1969. In this patent, it is proposed that the imbalance that could result from uneven placement of the two sets of coins along the opposite sides of the balance be minimized or negated by providing each arm of the balance at its outer end with an upwardly open cylindrical cup so that the coins in each set are stacked up on each arm just like a stack of poker chips.
The present invention has found it to be impossible to demonstrate the classical logical solution to the twelve coins problem using any practical available equipment. The difficulty encountered stems from the fact that in practice, unless expensive, precision equipment is used, the balance beam itself may not rest level on the fulcrum, the sites where the coins are to be placed on the two arms of the balance beam may not be exactly symmetrically located, and among the eleven "genuine" coins, which are nominally identical in weight, there are individual and unavoidable slight discrepancies.
As a result, in trying to demonstrate the classical solution to the problem with equipment of modest cost, it is impossible to tell, whether the beam is apparently imbalanced when it has a like number of coins on each arm or whether the set on the lower side includes a heavier counterfeit coin, or the set on the higher side includes a lighter counterfeit coin, or both sets include only "genuine" coins, but a random accumulation of individual deviations due to slight manufacturing variations has produced the seeming imbalance when, for the sake of the game, the beam should appear to be balanced.